# Fiches de cours

## Numerical analysis

#### Enseignant(s) :

Antolin Sanchez Pablo

English

#### Summary

This course offers an introduction to numerical methods for the solution of mathematical problems as: solution of systems of linear and non-linear equations, functions approximation, integration and differentiation and solution of differential equations.

#### Content

• Iterative methods for solving non-linear equations.
• Polynomial approximation: interpolation and least square methods.
• Numerical integration and differentiation.
• Solution of systems of linear equations: direct and iterative methods.
• Numerical approximation of differential equations.
• Introduction to MATLAB/OCTAVE software.

#### Keywords

Numerical algorithms; polynomial interpolation; numerical integration; numerical linear algebra; numerical solution of ODEs; iterative methods.

#### Learning Prerequisites

##### Required courses

Analyse, Algèbre linéaire

##### Important concepts to start the course

Analysis, linear algebra and programming.

#### Learning Outcomes

By the end of the course, the student must be able to:
• Choose a numerical method for solving a specific problem.
• Interpret obtained numerical results from a theoretical perspective.
• Estimate numerical errors.
• Prove theoretical properties of numerical methods.
• Implement numerical algorithms.
• Apply numerical algorithms to specific problems.
• Describe numerical methods.
• State theoretical properties of mathematical problems and numerical methods.

#### Transversal skills

• Use a work methodology appropriate to the task.
• Use both general and domain specific IT resources and tools
• Access and evaluate appropriate sources of information.

#### Teaching methods

Ex cathedra lectures; exercises in class and with computer using MATLAB/OCTAVE sofware.

#### Expected student activities

• Class attendance.
• Solution of exercises.
• Solution of problems using MATLAB/OCTAVE sofware.

#### Assessment methods

The exam may require to use a computer and MATLAB/OCTAVE software.

#### Supervision

 Office hours Yes Assistants Yes Forum No

#### Resources

Yes

##### Bibliography

In English:

• Lecturer notes.
• A. Quarteroni et F. Saleri et P. Gervasio: « Scientific Computing with MATLAB and OCTAVE », Springer, 2014, ISBN 978-3-642-45367-0.
• A. Quarteroni, R. Sacco et F. Saleri : « Numerical Mathematics », Springer, 2007, ISBN 978-3-540-49809-4.

In French:

• Lecture notes.
• A. Quarteroni, P. Gervasio et F. Saleri : « Calcul Scientifique : Cours, exercices corrigés et illustrations en MATLAB et OCTAVE », Springer, 2010, ISBN 978-88-470-1676-7.
• A. Quarteroni, R. Sacco et F. Saleri : « Méthodes Numériques - Algorithmes, analyse et applications », Springer, 2007, ISBN 978-88-470-0495-5.
• J. Rappaz et M. Picasso: "Introduction à l'analyse numérique", PPUR - Collection: Enseignement des mathématiques - 2em édition - 2011

##### Notes/Handbook

Lecture notes will be provided.

### Dans les plans d'études

• Semestre
Automne
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
Numerical analysis
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
1 Heure(s) hebdo x 14 semaines
• Passerelle HES - SIE, 2018-2019, Semestre automne
• Semestre
Automne
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
Numerical analysis
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
1 Heure(s) hebdo x 14 semaines
• Semestre
Automne
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
Numerical analysis
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
1 Heure(s) hebdo x 14 semaines

### Semaine de référence

LuMaMeJeVe
8-9    ELA1
9-10
10-11    CO4
CO5
CO6
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22

Cours
Exercice, TP
Projet, autre

### légende

• Semestre d'automne
• Session d'hiver
• Semestre de printemps
• Session d'été
• Cours en français
• Cours en anglais
• Cours en allemand